Truth-Conditional Accounts of Indicative Conditionals

This paper is a guide to the main ideas and innovations in Robert Stalnaker's "Indicative Conditionals". The paper is for a volume of essays on twenty-one classics of formal semantics edited by Louise McNally, Yael Sharvit and Zoltàn Gendler Szabò.

Richard Bradley offers a quick and convincing argument that no Boolean semantic theory for conditionals can validate a very natural principle concerning the relationship between cre- dences and conditionals. We argue that Bradley’s principle, Preservation, is, in fact, invalid; its appeal arises from the validity of a nearby, but distinct, principle, which we call Local Preservation, and which Boolean semantic theories can non-trivially validate.

A part of Stalnaker (1968)’s influential theory of conditionals has been neglected, namely the role for an accessibility relation between worlds. I argue that the accessibility relation does not play the role intended for it in the theory as stated, and propose a minimal revision which solves the problem, and brings the theory in line with the formulation in Stalnaker & Thomason 1970.

Language theorists have recently come to have an increasing appreciation for the fact that context contributes heavily in determining our interpretation of what is said. Indeed, it now seems clear that no complete understanding of a natural language is possible without some account of the way in which context affects our interpretation of discourse. In this paper, I will attempt to explore one facet of the language – context relationship, namely, the relation between conditionals and context. The first part of (...) the paper develops an account of truth for conditionals which allows them to depend on momentary features of the context in which they are uttered. In the second half of the paper, comparisons with other recent theories of the conditional will be considered. Particular attention will be given to the problem of whether the conditional really violates classical inferences such as Hypothetical Syllogism and Contraposition as has often been claimed in recent years. (shrink)

Sobel sequences have had a huge impact on the discussion of counterfactuals. They can be composed of conditionals and mere descriptions. What is especially puzzling about them is that they are often felicitously uttered when their reversal is not. Up to now, there is no unified explanation. I examine two strategies. We might begin with conditionals and proceed to descriptions. Or we might begin with descriptions and proceed to conditionals. I argue for the latter variant and outline a universal theory (...) of Sobel sequences in terms of presuppositional anaphora. One relevant result is that the phenomenon neither counts against nor in favour of the simplified standard account of counterfactuals à la Stalnaker-Lewis. (shrink)

Brogaard and Salerno (2008) argued that counter-examples to contraposition, strengthening the antecedent, and hypothetical syllogism involving subjunctive conditionals only seem to work because they involve a contextual fallacy where the context assumed in the premise(s) is illicitly shifted in the conclusion. To avoid such counter-examples they have proposed that the context must remain fixed when evaluating an argument for validity. That is the Brogaard-Salerno Stricture. Tristan Haze (2016), however, has recently objected that intuitively valid argumentative forms such as conjunction introduction (...) do not satisfy this constraint. This paper has two goals. First, it argues that the Brogaard-Salerno Stricture is not violated in Haze’s putative counter-example. Second, it argues that since this stricture blocks the usual counter-examples to instances of classical argumentative forms that involve indicative or subjunctive conditionals, it is reasonable to infer that indicative and subjunctive conditionals are material. (shrink)

The truth-functional hypothesis states that indicative conditional sentences and the material implication have the same truth conditions. Haze (2011) has rejected this hypothesis. He claims that a self-referential conditional, coupled with a plausible assumption about its truth-values and the assumption that the truth-functional hypothesis is true, lead to a liar’s paradox. Given that neither the self-referential conditional nor the assumption about its truth-values are problematic, the culprit of the paradox must be the truth-functional hypothesis. Therefore, we should reject it. In (...) this paper I argue that, contrary to what Haze thinks, the truth-functional hypothesis is not to blame. In fact, no liar’s paradox emerges when the truth-functional hypothesis is true; it emerges only if it is false. (shrink)

I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals. I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.

A uniform theory of conditionals is one which compositionally captures the behavior of both indicative and subjunctive conditionals without positing ambiguities. This paper raises new problems for the closest thing to a uniform analysis in the literature (Stalnaker, Philosophia, 5, 269–286 (1975)) and develops a new theory which solves them. I also show that this new analysis provides an improved treatment of three phenomena (the import-export equivalence, reverse Sobel-sequences and disjunctive antecedents). While these results concern central issues in the study (...) of conditionals, broader themes in the philosophy of language and formal semantics are also engaged here. This new analysis exploits a dynamic conception of meaning where the meaning of a symbol is its potential to change an agent’s mental state (or the state of a conversation) rather than being the symbol’s content (e.g. the proposition it expresses). The analysis of conditionals is also built on the idea that the contrast between subjunctive and indicative conditionals parallels a contrast between revising and consistently extending some body of information. (shrink)

Grice argues that indicative conditionals ‘if p then q’ have conventional, truth conditional meaning according to the material conditional ‘p  q’. In order to explain away the known paradoxes with this interpretation, he distinguishes between truth conditions and assertion conditions, attempting to demonstrate that the assumed connection between ‘p’ and ‘q’ (the Indirectness Condition) is a conversational implicature; hence a matter only relevant for the assertion conditions of a conditional. This paper argues that Grice fails to demonstrate i) that (...) the Indirectness Condition is cancellable, hence a conversational implicature, ii) that the Indirectness Condition is not part of the conventional, truth-relevant meaning of ‘if’, and accordingly, iii) semantic or logical equivalence between indicative and material conditionals. (shrink)

I argue that taking the Practical Conditionals Thesis seriously demands a new understanding of the semantics of such conditionals. Practical Conditionals Thesis: A practical conditional [if A][ought] expresses B’s conditional preferability given A Paul Weirich has argued that the conditional utility of a state of affairs B on A is to be identified as the degree to which it is desired under indicative supposition that A. Similarly, exploiting the PCT, I will argue that the proper analysis of indicative practical conditionals (...) is in terms of what is planned, desired, or preferred, given suppositional changes to an agent’s information. Implementing such a conception of conditional preference in a semantic analysis of indicative practical conditionals turns out to be incompatible with any approach which treats the indicative conditional as expressing non-vacuous universal quantification over some domain of relevant antecedent-possibilities. Such analyses, I argue, encode a fundamental misunderstanding of what it is to be best, given some condition. The analysis that does the best vis-à-vis the PCT is, instead, one that blends a Context-Shifty account of indicative antecedents with an Expressivistic, or non-propositional, treatment of their practical consequents. (shrink)

No existing conditional semantics captures the dual role of 'if' in embedded interrogatives — 'X wonders if p' — and conditionals. This paper presses the importance and extent of this challenge, linking it to cross-linguistic patterns and other phenomena involving conditionals. Among these other phenomena are conditionals with multiple 'if'-clauses in the antecedent — 'if p and if q, then r' — and relevance conditionals — 'if you are hungry, there is food in the cupboard'. Both phenomena are shown to (...) be problematic for existing analyses. Surprisingly, the decomposition of conditionals needed to capture the link with interrogatives provides a new analysis that captures all three phenomena. The model-theoretic semantics offered here relies on a dynamic conception of meaning and compositionality, a feature discussed throughout. (shrink)

The aim of this paper is to clarify the truth-functional interpretation of the logical connective of the material implication. The importance of such clarification lies in the fact that it allows avoiding the supposed paradoxes introduced by C. I. Lewis (1918). I argue that an adequate understanding of the history and purposes of logic is enough to dissolve them away. The defense is based on an exposition of propositional compositionalism. To compare, I also present Stalnaker’s (1968) alternative that seeks to (...) explain the implicit concept of conditionality of conditionals assertions. In order to reinforce my aim I expound the twelve different meanings of ‘implication’ stated by Corcoran (1993) in order to hold that a proper understanding of these meanings allows us to avoid ambiguities and confusions. Finally, I expect to show that despite the possible alternatives, compositionalism is still the best explanation for the truth-functionality account of logical connectives. (shrink)

The material interpretation of conditionals is commonly recognized as involving some paradoxical results. I here argue that the truth functional approach to natural language is the reason for the inadequacy of this material interpretation, since the truth or falsity of some pair of statements ‘p’ and ‘q’ cannot per se be decisive for the truth or falsity of a conditional relation ‘if p then q’. This inadequacy also affects the ability of the overall formal system to establish whether or not (...) arguments involving conditionals are valid. I also demonstrate that the Paradox of Indicative Conditionals does not actually involve a paradox, but instead contains some paralogistic elements that make it appear to be a paradox. The discussion of the paradox in this paper further reveals that the material interpretation of conditionals adversely affects the treatment of disjunctions. -/- Much has been said about these matters in the literature that point in the same direction. However, there seems to be some reluctance against fully complying with the arguments against the truth functional account of conditionals, since many of the alternative accounts rely on the material conditional, or at least on an understanding of the conditional as a function of antecedent and consequent in a similar sense as the material conditional. My argument against truth functionality indicates that it may in general involve similar problems to treat conditionals as such functions, whether one deals with theories of truth, assertability or probability. (shrink)

Lee Archie argued that if any truth-values are consistently assigned to a natural language conditional for which modus ponens and modus tollens are valid argument forms and affirming the consequent is invalid, this conditional will have the same truth-conditions of a material implication. This argument is simple and it requires few and relatively uncontroversial assumptions. We show that it is possible to extend Archie´s argument to three and five-valued logics and still vindicate the same conclusion. This defense is simpler because (...) it requires fewer assumptions: even if you do not believe in bivalence and the classical negation operator you still have good reasons to accept that natural language conditionals and the material implication are logically equivalent. (shrink)

This paper deals with Austinian ifs of every stripe within classical logic. It is argued that they are truth-functional and the theory of conditional elements is used. Ellipsis is key. Corrects an error in Fulda (2010) in translation and therefore scope. -/- The PDF is made available gratis by the Publisher.

The truth functional account of conditional statements ‘if A then B’ is not only inadequate; it eliminates the very conditionality expressed by ‘if’. Focusing only on the truth-values of the statements ‘A’ and ‘B’ and different combinations of these, one is bound to miss out on the conditional relation expressed between them. All approaches that treat conditionals as functions of their antecedents and consequents will end up in some sort of logical atomism where causal matters simply are reduced to the (...) joint occurrence of A and B. (shrink)

In a series of articles, David Barnett (2006, 2009, 2010) has developed a general theory of conditionals. The grand aim is to reconcile the two main rivals: a suppositional and a truth-conditional view (Barnett 2006, 521). While I confine my critical discussion to counterfactuals, I will give some hints how they might spell trouble for his suppositional view in general.

Claims that necessary and sufficient conditions are not converse relations are discussed, as well as the related claim that If A, then B is not equivalent to A only if B . The analysis of alleged counterexamples has shown, among other things, how necessary and sufficient conditions should be understood, especially in the case of causal conditions, and the importance of distinguishing sufficient-cause conditionals from necessary-cause conditionals. It is concluded that necessary and sufficient conditions, adequately interpreted, are converse relations in (...) all cases. (shrink)

Varzi (2005) discussed 6 ways of symbolizing the sentence 'If Alf went to the movies then Beth went too, but only if she found a taxi-cab.' In the present reply, a seventh symbolization is offered, along with an analysis of the six alternatives discussed by Varzi.

I outline and motivate a way of implementing a closest world theory of indicatives, appealing to Stalnaker's framework of open conversational possibilities. Stalnakerian conversational dynamics helps us resolve two outstanding puzzles for a such a theory of indicative conditionals. The first puzzle -- concerning so-called 'reverse Sobel sequences' -- can be resolved by conversation dynamics in a theoryneutral way: the explanation works as much for Lewisian counterfactuals as for the account of indicatives developed here. Resolving the second puzzle, by contrast, (...) relies on the interplay between the particular theory of indicative conditionals developed here and Stalnakerian dynamics. The upshot is an attractive resolution of the so-called "Gibbard phenomenon" for indicative conditionals. (shrink)